Expectation Maximization in Matlab on Missing Data

I have to use EM to estimate the mean and covariance of the Gaussian distribution for each of the two classes. They have some missing attributes too.开发者_运维问答

Classes of each object is known. Therefore the problem basically reduces to fitting a gaussian model with missing element.

Which is the best library to use?

How is ECM Algorithm different from EM algorithm?

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If you have access to the Statistics Toolbox, you can use the GMDISTRIBUTION class to fit a Gaussian Mixture Model using the EM algorithm.

Here is an example:

%# sample dataset
load fisheriris
data = meas(:,1:2);
label = species;

%# fit GMM using EM
K = 2;
obj = gmdistribution.fit(data, K);

%# assign points to mixtures: argmax_k P(M(k)|data)
P = posterior(obj, data);
[~,mIDX] = max(P,[],2);

%# GMM components
obj.mu             %# means
obj.Sigma          %# covariances
obj.PComponents    %# mixture weights

%# visualize original data clusters
figure
gscatter(data(:,1), data(:,2), label)

%# visualize mixtures found
figure
gscatter(data(:,1), data(:,2), mIDX), hold on
ezcontour(@(x,y)pdf(obj,[x y]), xlim(), ylim())

If not, check out the excellent Netlab Toolbox, as it has GMM implementation.

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Thanks all.But I am using ecmnmle for estimating parameters and then obtaining distribution of marginals which is used later in bayes classification. It works pretty fine with accuracies of 0.9 and 0.69 on 2 classes.

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Please take a look at the PMTK toolkit

Here is the EM implementation (Fit a mixture of Gaussians where the data may have NaN entries)